Geometric concept of isokinetic constraint for a system of particles

Abstract

The paper deals with the geometric concept of mechanical systems of N particles. The systems are modelled on the Cartesian product R XN and its first jet prolongation J 1.R XN / D R TXN , where X is a 3-dimensional Riemannian manifold with a metric G. The kinetic energy T of the system of N-particles is interpreted by means of the weighted quadratic form NQ G associated with the weighted metric tensor G which arises from the original metric tensor G and the system of N particles m1; : : : ;mN . A requirement for the kinetic energy of the system of N particles to be constant is regarded as a nonholonomic, so-called isokinetic constraint and it is defined as a fibered submanifold T of the jet space R TXN endowed with a certain distribution C called canonical distribution, which has the meaning of generalized admissible displacements of the system of particles subject to the isokinetic constraint. Vector generators of the canonical distribution are found.